Global and Local Hydrodynamic Stability Analysis as a Tool for Combustor Dynamics Modeling

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Pedro Paredes ◽  
Steffen Terhaar ◽  
Kilian Oberleithner ◽  
Vassilis Theofilis ◽  
Christian Oliver Paschereit
Keyword(s):  
Stability Analysis ◽  
Flow Field ◽  
Prediction Models ◽  
Global Analysis ◽  
Local Analysis ◽  
Reacting Flow ◽  
Dynamics Modeling ◽  
Mean Flow ◽  
Global Mode ◽  
Precessing Vortex Core

Coherent flow structures in shear flows are generated by instabilities intrinsic to the hydrodynamic field. In a combustion environment, these structures may interact with the flame and cause unsteady heat release rate fluctuations. Prediction and modeling of these structures are thereby highly wanted for thermo-acoustic prediction models. In this work, we apply hydrodynamic linear stability analysis to the time-averaged flow field of swirl-stabilized combustors obtained from experiments. Recent fundamental investigations have shown that the linear eigenmodes of the mean flow accurately represent the growth and saturation of the coherent structures. In this work, biglobal and local stability analyses are applied to the reacting flow in an industry-relevant combustion system. Both the local and the biglobal analyses accurately predict the onset and structure of a self-excited global instability that is known in the combustion community as a precessing vortex core (PVC). However, only the global analysis accurately predicts a globally stable flow field for the case without the oscillation, while the local analysis wrongly predicts an unstable global growth rate. The predicted spatial distribution of the amplitude functions using both analyses agrees very well to the experimentally identified global mode. The presented tools are considered as very promising for the understanding of the PVC and physics based flow control.

Global and Local Hydrodynamic Stability Analysis as a Tool for Combustor Dynamics Modeling

2015 ◽  
Author(s):  
Pedro Paredes ◽  
Vassilis Theofilis ◽  
Steffen Terhaar ◽  
Kilian Oberleithner ◽  
Christian Oliver Paschereit
Keyword(s):  
Stability Analysis ◽  
Flow Field ◽  
Prediction Models ◽  
Global Analysis ◽  
Local Analysis ◽  
Reacting Flow ◽  
Dynamics Modeling ◽  
Mean Flow ◽  
Global Mode ◽  
Precessing Vortex Core

Coherent flow structures in shear flows are generated by instabilities intrinsic to the hydrodynamic field. In a combustion environment, these structures may interact with the flame and cause unsteady heat release rate fluctuations. Prediction and modeling of these structures is thereby highly wanted for thermo-acoustic prediction models. In this work we apply hydrodynamic linear stability analysis to the time-averaged flow field of swirl-stabilized combustors obtained from experiments. Recent fundamental investigations have shown that the linear eigenmodes of the mean flow accurately represent the growth and saturation of the coherent structures. In this work biglobal and local stability analysis is applied to the reacting flow in an industry-relevant combustion system. Both the local and the biglobal analysis accurately predicts the onset and structure of a self-excited global instability that is known in the combustion community as a precessing vortex core (PVC). However, only the global analysis accurately predicts a globally stable flow field for the case without the oscillation, while the local analysis wrongly predicts an unstable global growth rate. The predicted spatial distribution of the amplitude functions using both analysis agree very well to the experimentally identified global mode. The presented tools are considered as very promising for the understanding of the PVC and physics based flow control.

scholarly journals Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Miles Owen ◽  
Abdelkader Frendi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Global Analysis ◽  
Leading Edge ◽  
Local Analysis ◽  
Mean Flow

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

Why Non-Uniform Density Suppresses the Precessing Vortex Core

2013 ◽  
Author(s):  
Kilian Oberleithner ◽  
Steffen Terhaar ◽  
Lothar Rukes ◽  
Christian Oliver Paschereit
Keyword(s):  
Natural Gas ◽  
Vortex Core ◽  
Hydrodynamic Instability ◽  
Density Field ◽  
Density Stratification ◽  
Reacting Flow ◽  
Global Instability ◽  
Global Mode ◽  
Precessing Vortex Core ◽  
Flow Oscillations

Isothermal swirling jets undergoing vortex breakdown are known to be susceptible to self-excited flow oscillations. They manifest in a precessing vortex core and synchronized growth of large-scale vortical structures. Recent theoretical studies associate these dynamics with the onset of a global hydrodynamic instability mode. These global modes also emerge in reacting flows, thereby crucially affecting the mixing characteristics and the flame dynamics. It is, however, observed that these self-excited flow oscillations are often suppressed in the reacting flow, while they are clearly present at isothermal conditions. This study provides strong evidence that the suppression of the precessing vortex core is caused by density stratification created by the flame. This mechanism is revealed by considering two reacting flow configurations: The first configuration represents a detached steam-diluted natural gas swirl-stabilized flame featuring a strong precessing vortex core. The second represents a natural gas swirl-stabilized flame anchoring near the combustor inlet, which does not exhibit self-excited oscillations. Experiments are conducted in a generic combustor test rig and the flow dynamics are captured using PIV and LDA. The corresponding density fields are approximated from the seeding density using a quantitative light sheet technique. The experimental results are compared to the global instability properties derived from hydrodynamic linear stability theory. Excellent agreement between the theoretically derived global mode frequency and measured precession frequency provide sufficient evidence to conclude that the self-excited oscillations are, indeed, driven by a global hydrodynamic instability. The effect of the density field on the global instability is studied explicitly by performing the analysis with and without density stratification. It turns out that the significant change on instability is caused by the radial density gradients in the inner recirculation zone and not by the change of the mean velocity field. The present work provides a theoretical framework to analyze the global hydrodynamic instability of realistic combustion configurations. It allows relating the flame position and the resulting density field to the emergence of a precessing vortex core.

scholarly journals Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

2017 ◽  
Author(s):  
Thomas L. Kaiser ◽  
Thierry Poinsot ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Large Eddy Simulations ◽  
Mode Shapes ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Large Eddy ◽  
Good Agreement

The hydrodynamic instability in an industrial, two-staged, counter-rotative, swirled injector of highly complex geometry is under investigation. Large eddy simulations show that the complicated and strongly nonparallel flow field in the injector is superimposed by a strong precessing vortex core. Mean flow fields of large eddy simulations, validated by experimental particle image velocimetry measurements are used as input for both local and global linear stability analysis. It is shown that the origin of the instability is located at the exit plane of the primary injector. Mode shapes of both global and local linear stability analysis are compared to a dynamic mode decomposition based on large eddy simulation snapshots, showing good agreement. The estimated frequencies for the instability are in good agreement with both the experiment and the simulation. Furthermore, the adjoint mode shapes retrieved by the global approach are used to find the best location for periodic forcing in order to control the precessing vortex core.

Time-Resolved PIV Measurements of Non-Reacting Flow Field in a Swirl-Stabilized Combustor Without and With Porous Inserts for Acoustic Control

2014 ◽  
Author(s):  
Joseph Meadows ◽  
Ajay K. Agrawal
Keyword(s):  
Flow Field ◽  
Direct Injection ◽  
Combustion Noise ◽  
Reacting Flow ◽  
Turbulent Structures ◽  
Time Resolved ◽  
Turbulence Structures ◽  
Precessing Vortex Core ◽  
Acoustic Control ◽  
Acoustic Instabilities

Combustion noise and thermo-acoustic instabilities are of primary importance in highly critical applications such as rocket propulsion systems, power generation, and jet propulsion engines. Mechanisms for combustion instabilities are extremely complex because they often involve interactions among several different physical phenomena such as unsteady flame propagation leading to unsteady flow field, acoustic wave propagation, natural and forced hydrodynamic instabilities, etc. In the past, we have utilized porous inert media (PIM) to mitigate combustion noise and thermo-acoustic instabilities in both lean premixed (LPM) and lean direct injection (LDI) combustion systems. While these studies demonstrated the efficacy of the PIM concept to mitigate noise and thermo-acoustic instabilities, the actual mechanisms involved have not been understood. The present study utilizes time-resolved particle image velocimetry to measure the turbulent flow field in a non-reacting swirl-stabilized combustor without and with PIM. Although the flow field inside the annulus of the PIM cannot be observed, measurements immediately downstream of the PIM provide insight into the turbulent structures. Results are analyzed using the Proper Orthogonal Decomposition (POD) method and show that the PIM alters the flow field in an advantageous manner by modifying the turbulence structures and eliminating the corner recirculation zones and precessing vortex core, which would ultimately affect the acoustic behavior in a favorable manner.

Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction

2011 ◽  
Vol 679 ◽  
pp. 383-414 ◽  
Author(s):  
K. OBERLEITHNER ◽  
M. SIEBER ◽  
C. N. NAYERI ◽  
C. O. PASCHEREIT ◽  
C. PETZ ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Coherent Structures ◽  
Vortex Breakdown ◽  
Particle Image Velocimetry Data ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Helical Structures ◽  
Global Mode ◽  
Swirling Jet ◽  
Time Periodic

The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.

Why Nonuniform Density Suppresses the Precessing Vortex Core

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Kilian Oberleithner ◽  
Steffen Terhaar ◽  
Lothar Rukes ◽  
Christian Oliver Paschereit
Keyword(s):  
Linear Stability ◽  
Vortex Core ◽  
Hydrodynamic Instability ◽  
Density Field ◽  
Sufficient Evidence ◽  
Reacting Flow ◽  
Global Instability ◽  
Global Mode ◽  
Precessing Vortex Core ◽  
Flow Oscillations

Linear stability analysis is applied to a swirl-stabilized combustor flow with the aim to understand how the flame shape and associated density field affects the manifestation of self-excited flow instabilities. In isothermal swirling jets, self-excited flow oscillations typically manifest in a precessing vortex core and synchronized growth of large-scale spiral-shaped vortical structures. Recent theoretical studies relate these dynamics to a hydrodynamic global instability. These global modes also emerge in reacting flows, thereby crucially affecting the mixing characteristics and the flame dynamics. It is, however, observed that these self-excited flow oscillations are often suppressed in the reacting flow, while they are clearly present at isothermal conditions. This study provides strong evidence that the suppression of the precessing vortex core is caused by density inhomogeneities created by the flame. This mechanism is revealed by considering two reacting flow configurations: The first configuration represents a perfectly premixed steam-diluted detached flame featuring a strong precessing vortex core. The second represents a perfectly premixed dry flame anchoring near the combustor inlet, which does not exhibit self-excited oscillations. Experiments are conducted in a generic combustor test rig and the flow dynamics are captured using PIV and LDA. The corresponding density fields are approximated from the seeding density using a quantitative light sheet technique. The experimental results are compared to the global instability properties derived from hydrodynamic linear stability theory. Excellent agreement between the theoretically derived global mode frequency and measured precession frequency provide sufficient evidence to conclude that the self-excited oscillations are, indeed, driven by a global hydrodynamic instability. The effect of the density field on the global instability is studied explicitly by performing the analysis with and without density stratification. It turns out that the significant change in instability is caused by the radial density gradients in the inner recirculation zone and not by the change of the mean velocity field. The present work provides a theoretical framework to analyze the global hydrodynamic instability of realistic combustion configurations. It allows for relating the flame position and the resulting density field to the emergence of a precessing vortex core.

scholarly journals Modal Analysis of a Laminar-Flow Airfoil under Buffet Conditions at Re = 500,000

2019 ◽  
Vol 104 (2-3) ◽  
pp. 509-532 ◽  
Author(s):  
Markus Zauner ◽  
Neil D. Sandham
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Prediction Models ◽  
Angle Of Attack ◽  
Dynamic Mode ◽  
Mean Flow ◽  
Global Mode ◽  
Moderate Reynolds Number ◽  
Shock Motion ◽  
Transonic Buffet

AbstractAn airfoil undergoing transonic buffet exhibits a complex combination of unsteady shock-wave and boundary-layer phenomena, for which prediction models are deficient. Recent approaches applying computational fluid mechanics methods using turbulence models seem promising, but are still unable to answer some fundamental questions on the detailed buffet mechanism. The present contribution is based on direct numerical simulations of a laminar flow airfoil undergoing transonic buffet at Mach number M = 0.7 and a moderate Reynolds number Re = 500, 000. At an angle of attack α = 4∘, a significant change of the boundary layer stability depending on the aerodynamic load of the airfoil is observed. Besides Kelvin Helmholtz instabilities, a global mode, showing the coupled acoustic and flow-separation dynamics, can be identified, in agreement with literature. These modes are also present in a dynamic mode decomposition (DMD) of the unsteady direct numerical solution. Furthermore, DMD picks up the buffet mode at a Strouhal number of St = 0.12 that agrees with experiments. The reconstruction of the flow fluctuations was found to be more complete and robust with the DMD analysis, compared to the global stability analysis of the mean flow. Raising the angle of attack from α = 3∘ to α = 4∘ leads to an increase in strength of DMD modes corresponding to type C shock motion. An important observation is that, in the present example, transonic buffet is not directly coupled with the shock motion.

Modeling Flame Describing Functions Based on Hydrodynamic Linear Stability Analysis

2016 ◽  
Author(s):  
Kilian Oberleithner ◽  
Christian Oliver Paschereit
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Stability ◽  
Prediction Models ◽  
Time Lag ◽  
Stationary Flow ◽  
High Amplitude ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flame Response ◽  
Lag Model

Combustion instabilities crucially affect the operational range of modern lean premixed gas turbine combustors and must be avoided or kept at low amplitudes. The main uncertainty of current prediction models is the flame describing function (FDF) that characterizes the flame response to high amplitude acoustic forcing. In this work, we present a new FDF model based on linear hydrodynamic stability analysis. This work is in continuation of an earlier study, where the frequency dependence and saturation of the FDF gain of a perfectly premixed flame was linked to the growth rates of the Kelvin–Helmholtz (KH) instability. In this work, we report on FDF measurements in a newly designed swirl-stabilized combustor. We identify two independent mechanisms that determine the flame response. The first stems from swirl-fluctuations that are generated in the swirler and the second stems from the KH instability. The swirl-fluctuations are approximated by a convective time lag model. The KH instability is predicted from linear hydrodynamic stability analysis based on the time-mean flow measured via PIV. A combination of both models leads to a good quantitative agreement with the measured FDF. Besides the practical advantages of predicting the FDF from stationary flow data, the model reveals the mechanisms driving the saturation of the FDF and guides the way out from the black-box treatment of the nonlinear flame response.

Guiding Actuator Designs for Active Flow Control of the Precessing Vortex Core by Adjoint Linear Stability Analysis

2018 ◽  
Author(s):  
Jens S. Müller ◽  
Finn Lückoff ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Combustion Chamber ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Stereoscopic Particle Image Velocimetry ◽  
Axial Position ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Lock In

The fundamental impact of the precessing vortex core (PVC) as a dominant coherent flow structure in the flow field of swirl-stabilized gas turbine combustors has still not been investigated in depth. In order to do so, the PVC needs to be actively controlled to be able to set its parameters independently to any other of the combustion system. In this work, open-loop actuation is applied in the mixing section between the swirler and the generic combustion chamber of a non-reacting swirling jet setup to investigate the receptivity of the PVC with regard to its lock-in behavior at different streamwise positions. The mean flow in the mixing section as well as in the combustion chamber is measured by stereoscopic particle image velocimetry and the PVC is extracted from the snapshots using proper orthogonal decomposition. The lock-in experiments reveal the axial position in the mixing section that is most suitable for actuation. Furthermore, a global linear stability analysis is conducted to determine the adjoint mode of the PVC which reveals the regions of highest receptivity to periodic actuation based on mean flow input only. This theoretical receptivity model is compared with the experimentally obtained receptivity data and the applicability of the adjoint-based model for the prediction of optimal actuator designs is discussed.

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